The cutoff wavenumbers of elliptical waveguides were calculated by using isogeomtric analysis method (IGA). With NURBS basis functions in IGA, the computational model was consistent with geometric model imported from CAD system. The field variable (longitudinal electric/magnetic field) was constructed by the same NURBS basis functions as the representation of geometric model. In the refinement procedure used to get a more accurate solution, communication with original CAD system is unnecessary and the geometric shape is kept unchanged. The Helmholtz equation is weakened to a set of general eigenvalue equation by virtual work principal with discretized degree-of-freedom on control points. Elliptical waveguides with three typical eccentricities, 0.1, 0.5 and 0.9, are calculated by IGA with different size mesh. The first four cutoff wavenumbers are obtained even in coarse mesh and the RMS of first 25 cutoff wavenumbers has much more swift convergence rate with decreasing the mesh size than traditional FEM. The accuracy and robustness of the proposed method are validated by elliptical waveguides, and also the method can be applied to waveguides with arbitrary cross sections.
基于比例边界有限元法(scaled boundary finite element method,SBFEM)对结构-无限地基系统进行了频域的动力相互作用分析。通过一种新的高阶透射边界对无限地基进行模拟,该透射边界是基于无限域动力刚度矩阵的连分式解形式,连分式的系数通过以动力刚度矩阵表示的比例边界有限元方程递推计算。通过数值算例验证了该高阶透射边界的收敛性,并与解析解进行了比较,表明该方法具有较高的精度。最后对重力坝-库水-无限地基系统进行了频域分析,将计算结果与无质量地基模型进行了对比。对比结果表明,所提地基模型计算的结果与无质量地基模型的计算结果相比降低约20%。该方法可以有效地进行二维和三维大型结构-地基相互作用分析。
The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.
A new numerical method,scaled boundary isogeometric analysis(SBIGA)combining the concept of the scaled boundary finite element method(SBFEM)and the isogeometric analysis(IGA),is proposed in this study for 2D elastostatic problems with both homogenous and inhomogeneous essential boundary conditions.Scaled boundary isogeometric transformation is established at a specified scaling center with boundary isogeometric representation identical to the design model imported from CAD system,which can be automatically refined without communication with the original system and keeping geometry invariability.The field variable,that is,displacement,is constructed by the same basis as boundary isogeometric description keeping analytical features in radial direction.A Lagrange multiplier scheme is suggested to impose the inhomogeneous essential boundary conditions.The new proposed method holds the semi-analytical feature inherited from SBFEM,that is,discretization only on boundaries rather than the entire domain,and isogeometric boundary geometry from IGA,which further increases the accuracy of the solution.Numerical examples,including circular cavity in full plane,Timoshenko beam with inhomogenous boundary conditions and infinite plate with circular hole subjected to remotely tension,demonstrate that SBIGA can be applied efficiently to elastostatic problems with various boundary conditions,and powerful in accuracy of solution and less degrees of freedom(DOF)can be achieved in SBIGA than other methods.
